The organization of bristles on the Drosophila notum has long served as a popular model of robust tissue patterning. During this process, membrane-tethered Delta activates intracellular Notch signaling in neighboring epithelial cells, which inhibits Delta expression. This induces lateral inhibition, yielding a pattern in which each Delta-expressing mechanosensory organ precursor cell in the epithelium is surrounded on all sides by cells with active Notch signaling. Here, we show that conventional models of Delta-Notch signaling cannot account for bristle spacing or the gradual refinement of this pattern. Instead, the pattern refinement we observe using live imaging is dependent upon dynamic, basal actin-based filopodia and can be quantitatively reproduced by simulations of lateral inhibition incorporating Delta-Notch signaling by transient filopodial contacts between nonneighboring cells. Significantly, the intermittent signaling induced by these filopodial dynamics generates a type of structured noise that is uniquely suited to the generation of well-ordered, tissue-wide epithelial patterns.